HVPG TRT and Power Analysis
Aims
Here, I will analyse the HVPG dataset, evaluate aspects of its test-retest reliability, and perform a power analysis for comparing treatments.
Libraries
library(tidyverse)
library(relfeas)
library(readxl)
library(hrbrthemes)
library(extrafont)
library(lme4)
library(lmerTest)
library(effsize)
library(broom)
library(RColorBrewer)
library(knitr)
library(cowplot)
library(progress)
library(kableExtra)
library(perm)
library(ggbeeswarm)
library(psych)
library(permuco)
library(metafor)
library(viridis)
library(pwr)
extrafont::loadfonts(quiet = T)
theme_set(theme_ipsum_rc())
nsims <- 1e4
overwrite <- FALSE
knitr::opts_chunk$set(fig.path = "figures/", dev="png", dpi=600,
warning=FALSE, message=FALSE)
set.seed(42)Data
trt_tidy <- read_excel("../RawData/TEST_RETEST_FINA_DATABASE_TIDY.xlsx") %>%
mutate(author = str_match(Description, "(^\\w*)")[,2]) %>%
select(-contains("≦"))
trt_wide <- read_excel("../RawData/TEST_RETEST_FINA_DATABASE.xlsx") %>%
select(New_Description, `Serial number`) %>%
select(-contains("≦"))
trt_studydemog <- read_excel("../RawData/FINAL_AGGREGATED_ICCs-2.xlsx") %>%
select(Study, Perc_Alc, Perc_Decomp, Days=TIMEDAYS,
Centre = CENTER,
n_Patients = NUMBEROFPATIENTs) %>%
mutate(Centre = ifelse(Centre == 1, yes = "Multi-centre", "Single-centre"))Now let’s add the new new description to the trt_tidy sheet
trt_tidy <- trt_tidy %>%
left_join(trt_wide)Study Names
studynames <- trt_tidy %>%
select(Study = New_Description,
Technique = `Technique - Balloon/ catheter`) %>%
unique() %>%
mutate(Technique = ifelse(Technique=="Wedged Catheter",
yes = "Wedged Catheter",
no = "Balloon-tipped Catheter")) %>%
mutate(Technique = ifelse(is.na(Technique),
yes = "Balloon-tipped Catheter",
no = Technique)) %>%
mutate(Catheter = ifelse(Technique=="Wedged Catheter",
yes="Wedged", no="Balloon tip"))Test-Retest Analysis
As if one study
Now, we look at the data as if it were all one study, however we also divide by whether the study contains decompensated patients.
trt_all <- trt_tidy %>%
filter(Description != "Spahr. Octreotide") %>%
select(-Study) %>%
rename(Study= New_Description) %>%
left_join(trt_studydemog) %>%
mutate(decomp = ifelse(Perc_Decomp >0 ,
yes="Includes Decompensated",
no = "Only Compensated")) %>%
group_by(decomp) %>%
nest() %>%
mutate(trt = map(data, ~relfeas::trt(data = .x,
values='PP',
cases = "Serial number",
rater = 'MEASUREMENT' )$tidy)) %>%
select(-data) %>%
unnest(trt)
trt_allsaveRDS(trt_all, "../Cluster/trt_all.rds")
kable(trt_all, digits=2)I’ll also create a tidy version of this to complement the individual studies.
trt_all_tidy <- trt_all %>%
mutate(signvar_sd = signvar_sd * mean) %>%
ungroup() %>%
select(Patients = decomp,
Mean = mean, CV = cv,
WSCV = wscv, ICC = icc,
SDD = sdd,
"Change SD" = signvar_sd) %>%
arrange(desc(Patients))
kable(trt_all_tidy, digits=2)So, overall, we estimate that our smallest detectable difference in an individual is 4.3mmHg for only compensated patients, and 5.2mmHg for studies including decompensated patients
trt_all_detailed <- trt_tidy %>%
filter(Description != "Spahr. Octreotide") %>%
select(-Study) %>%
rename(Study= New_Description) %>%
left_join(trt_studydemog) %>%
mutate(decomp = ifelse(Perc_Decomp >0 ,
yes="Includes Decompensated",
no = "Only Compensated")) %>%
filter(Description != "Spahr. Octreotide") %>%
group_by(decomp) %>%
nest() %>%
mutate(trt = map(data, ~relfeas::trt(data = .x,
values='PP',
cases = "Serial number",
rater = 'MEASUREMENT' )))
trt_all_detailed$decomp[1]## [1] "Includes Decompensated"trt_all_detailed$trt[[1]]$sdd## $value
## [1] 5.15761
##
## $lbound
## [1] 4.657455
##
## $ubound
## [1] 5.77906trt_all$sdd_l <- trt_all_detailed$trt[[1]]$sdd$lbound
trt_all$sdd_u <- trt_all_detailed$trt[[1]]$sdd$ubound
trt_all_detailed$decomp[2]## [1] "Only Compensated"trt_all_detailed$trt[[2]]$sdd## $value
## [1] 4.293093
##
## $lbound
## [1] 3.802727
##
## $ubound
## [1] 4.929798trt_all$sdd_l[2] <- trt_all_detailed$trt[[2]]$sdd$lbound
trt_all$sdd_u[2] <- trt_all_detailed$trt[[2]]$sdd$ubound
trt_all_detailed$decomp[1]## [1] "Includes Decompensated"trt_all_detailed$trt[[1]]$sddm## $value
## [1] 0.2978477
##
## $lbound
## [1] 0.2656889
##
## $ubound
## [1] 0.3344565trt_all$sddm <- trt_all_detailed$trt[[1]]$sddm$value*100
trt_all$sddm_l <- trt_all_detailed$trt[[1]]$sddm$lbound*100
trt_all$sddm_u <- trt_all_detailed$trt[[1]]$sddm$ubound*100
trt_all_detailed$decomp[2]## [1] "Only Compensated"trt_all_detailed$trt[[2]]$sddm## $value
## [1] 0.2618087
##
## $lbound
## [1] 0.228803
##
## $ubound
## [1] 0.3000771trt_all$sddm[2] <- trt_all_detailed$trt[[2]]$sddm$value*100
trt_all$sddm_l[2] <- trt_all_detailed$trt[[2]]$sddm$lbound*100
trt_all$sddm_u[2] <- trt_all_detailed$trt[[2]]$sddm$ubound*100Now, let’s prepare this as a table for below the forest plot
overall_n <- map_dbl(trt_all_detailed$data, nrow)
overall <- trt_all %>%
ungroup() %>%
rename(Study = decomp) %>%
mutate(decomp = "Overall",
Catheter = "Balloon tip",
n = overall_n) %>%
arrange(desc(Study)) %>%
mutate(Study = ifelse(Study=="Includes Decompensated",
"Includes Decompensated*",
Study))
overallGrouped by study
trt_study <- trt_tidy %>%
group_by(New_Description) %>%
nest() %>%
mutate(outcomes = map(data, ~ trt( data=.x, values='PP',
cases = "Serial number", rater = 'MEASUREMENT' )))
trt_study <- trt_study %>%
mutate(n = map_dbl(data, nrow))
tidytrt <- map_df(trt_study$outcomes, 'tidy') %>%
mutate(n = trt_study$n) %>%
mutate(Study = trt_study$New_Description) %>%
select(Study, everything()) %>%
left_join(studynames) %>%
left_join(trt_studydemog) %>%
mutate(decomp = ifelse(Perc_Decomp >0 ,
yes="Includes Decompensated",
no = "Only Compensated")) %>%
mutate(decomp = fct_inorder(decomp)) %>%
select(-n_Patients)
knitr::kable(tidytrt, digits = 2)Now let’s make a table for the paper with the relevant things.
tidytrt_table <- tidytrt %>%
mutate(signvar_sd = signvar_sd * mean) %>%
select(decomp,
Study,
n,
"Decompensated (%)" = Perc_Decomp,
"Alcoholic (%)" = Perc_Alc,
"Mean Days Elapsed" = Days,
Mean = mean, CV = cv,
WSCV = wscv, ICC = icc,
SDD = sdd,
"Change SD" = signvar_sd) %>%
arrange(desc(decomp), Study)
decomp_change <- head(
which(
tidytrt_table$decomp == tail(tidytrt_table$decomp, 1)), 1 )
tidytrt_kable <- knitr::kable(tidytrt_table[,-1], digits=2) %>%
kable_styling("striped", full_width = F) %>%
pack_rows(head(tidytrt_table$decomp, 1), 1, decomp_change-1) %>%
pack_rows(tail(tidytrt_table$decomp, 1), decomp_change, nrow(tidytrt_table))
tidytrt_kable# save_kable(tidytrt_kable, file = "figures/tidytrt_kable.jpg")ICC
Let’s have a look at the ICC as a measure of between-subject differentiability (i.e. reliability).
icc_out <- select(tidytrt, Study, icc, icc_l, icc_u, decomp, n) %>%
left_join(studynames) %>%
mutate(decomp = factor(decomp, levels=c(
"Includes Decompensated", "Only Compensated"))) %>%
arrange(decomp, icc) %>%
bind_rows(overall) %>%
mutate(Study = fct_inorder(Study))
ICCs <- ggplot(icc_out,aes(x=icc,y=Study,
colour=Catheter)) +
#geom_rect(aes(xmin=0.8, xmax=1, ymin=-Inf, ymax=Inf),
# alpha = .1, fill="grey", colour="grey") +
facet_grid(decomp~., scales="free", space="free") +
geom_point(aes(size=log(n)), shape=18) +
scale_x_continuous(breaks = seq(0, 1, by=0.2))+
geom_errorbarh(aes(xmax = icc_u, xmin = icc_l), height = 0.2) +
#geom_vline(xintercept = 1, linetype = "longdash") +
labs(y="", x="Intraclass Correlation Coefficient (ICC)") +
theme(text = element_text(size=20)) +
ggtitle("ICC (95% CI)") +
scale_colour_manual(values = c("black", "red")) +
coord_cartesian(xlim = c(-0.1, 1)) +
#ylim = c(0,12)) +
guides(size = FALSE) +
NULL
ICCs + theme(legend.position = "none")
This analysis constitutes a mega-analysis: we have all the original data and the overall estimates are performed using the original data estimates. However, in order to asess the study heterogeneity, I will run a classical meta-analysis. I will perform a Fisher’s z transformation on the ICC values, perform a classic meta-analysis, and assess the heterogeneity.
dat <- icc_out %>%
filter(Study != "Spahr 2007") %>%
filter(decomp != "Overall") %>%
filter(n > 4) %>%
escalc(measure="ZCOR", ri=icc, ni=n, data=., slab=Study)
res <- rma(yi, vi, data=dat)
res ##
## Random-Effects Model (k = 20; tau^2 estimator: REML)
##
## tau^2 (estimated amount of total heterogeneity): 0.1838 (SE = 0.0768)
## tau (square root of estimated tau^2 value): 0.4287
## I^2 (total heterogeneity / total variability): 81.58%
## H^2 (total variability / sampling variability): 5.43
##
## Test for Heterogeneity:
## Q(df = 19) = 91.7982, p-val < .0001
##
## Model Results:
##
## estimate se zval pval ci.lb ci.ub
## 1.2674 0.1091 11.6164 <.0001 1.0536 1.4813 ***
##
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1SDD
Absolute
Let’s have a look at the study-by-study SDD, but in raw units
sdd_out <- map_df(trt_study$outcomes, "sdd") %>%
mutate(Study = trt_study$New_Description) %>%
rename(sdd=value, sdd_l = lbound, sdd_u = ubound) %>%
left_join(studynames) %>%
left_join(select(tidytrt, Study, decomp, n)) %>%
left_join(trt_studydemog) %>%
mutate(decomp = ifelse(Perc_Decomp >0 ,
yes="Includes Decompensated",
no = "Only Compensated")) %>%
mutate(decomp = factor(decomp, levels=c(
"Includes Decompensated", "Only Compensated"))) %>%
arrange(decomp, desc(sdd)) %>%
bind_rows(overall) %>%
mutate(Study = fct_inorder(Study))
SDDs <- ggplot(sdd_out,aes(x=sdd,y=Study,
colour=Catheter)) +
facet_grid(decomp~., scales="free", space="free") +
geom_point(aes(size=log(n)), shape=18) +
scale_x_continuous(breaks = seq(0, 20, by=2))+
geom_errorbarh(aes(xmax = sdd_u, xmin = sdd_l), height = 0.15) +
#geom_vline(xintercept = 1, linetype = "longdash") +
labs(y="", x="Smallest Detectable Difference (mmHg)") +
theme(text = element_text(size=20)) +
ggtitle("SDD (95% CI)") +
scale_colour_manual(values = c("black", "red")) +
guides(colour=FALSE, shape=FALSE) +
#scale_shape_manual(values = c(18, 19)) +
coord_cartesian(xlim=c(0,16)) +
guides(size = FALSE) +
NULL
SDDs #+ annotate("rect", xmin = 0.75, xmax = 1, ymin="Spahr 2007", ymax="Blei 1987", alpha = .2, fill="grey")
And here we run the meta-analysis again to assess heterogeneity. We can’t use the SDD because it has asymmetric confidence intervals, and it cannot be Fisher’s z transformed. So we can run a meta-analysis based on the average absolute variation to test the heterogeneity.
dat <- trt_study %>%
mutate(
mean_abs_var = map_dbl(outcomes, ~mean(sqrt(.x$absvars))),
se_abs_var = map_dbl(outcomes, ~sd(sqrt(.x$absvars)) / sqrt(length(.x$absvars)))
) %>%
filter(New_Description != "Spahr 2007") %>%
ungroup() %>%
mutate(
yi = mean_abs_var,
vi = se_abs_var^2) %>%
select(-data, -outcomes) %>%
escalc(measure="MN", yi=yi, vi=vi, ni=n, data=., slab=New_Description)
transf.sqrt <- function (xi, ...)
{
zi <- sqrt(xi)
zi[xi < 0] <- 0
return(c(zi))
}
res <- rma(yi, vi, data=dat)
res ##
## Random-Effects Model (k = 21; tau^2 estimator: REML)
##
## tau^2 (estimated amount of total heterogeneity): 0.0016 (SE = 0.0010)
## tau (square root of estimated tau^2 value): 0.0405
## I^2 (total heterogeneity / total variability): 54.64%
## H^2 (total variability / sampling variability): 2.20
##
## Test for Heterogeneity:
## Q(df = 20) = 46.5104, p-val = 0.0007
##
## Model Results:
##
## estimate se zval pval ci.lb ci.ub
## 0.2572 0.0128 20.1232 <.0001 0.2322 0.2823 ***
##
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1Percentage
Now the study-by-study SDD, but in percentages
sddm_out <- map_df(trt_study$outcomes, "sddm") %>%
mutate(Study = trt_study$New_Description) %>%
rename(sddm=value, sddm_l = lbound, sddm_u = ubound) %>%
mutate(sddm=100*sddm, sddm_l = 100*sddm_l, sddm_u = 100*sddm_u) %>%
left_join(studynames) %>%
left_join(select(tidytrt, Study, decomp, n)) %>%
left_join(trt_studydemog) %>%
mutate(decomp = ifelse(Perc_Decomp >0 ,
yes="Includes Decompensated",
no = "Only Compensated")) %>%
mutate(decomp = factor(decomp, levels=c(
"Includes Decompensated", "Only Compensated"))) %>%
arrange(decomp, desc(sddm)) %>%
bind_rows(overall) %>%
mutate(Study = fct_inorder(Study))
SDDms <- ggplot(sddm_out,aes(x=sddm,y=Study,
colour=Catheter)) +
facet_grid(decomp~., scales="free", space="free") +
geom_point(aes(size=log(n)), shape=18) +
scale_x_continuous(breaks = seq(0, 80, by=10))+
geom_errorbarh(aes(xmax = sddm_u, xmin = sddm_l), height = 0.15) +
#geom_vline(xintercept = 1, linetype = "longdash") +
labs(y="", x="Smallest Detectable Difference (%mmHg)") +
theme(text = element_text(size=20)) +
ggtitle("%SDD (95% CI)") +
scale_colour_manual(values = c("black", "red")) +
guides(colour=FALSE, shape=FALSE) +
#scale_shape_manual(values = c(18, 19)) +
coord_cartesian(xlim=c(0,80)) +
guides(size = FALSE) +
NULL
SDDms #+ annotate("rect", xmin = 0.75, xmax = 1, ymin="Spahr 2007", ymax="Blei 1987", alpha = .2, fill="grey")
And here we run the meta-analysis to assess heterogeneity. We can’t use the SDD% because it has asymmetric confidence intervals, and it cannot be Fisher’s z transformed. So we can run a meta-analysis based on the average absolute percentage variation to test the heterogeneity.
dat <- trt_study %>%
mutate(
mean_abs_var = map_dbl(outcomes, ~mean(sqrt(.x$absvars / .x$means))),
se_abs_var = map_dbl(outcomes, ~sd(sqrt(.x$absvars / .x$means)) /
sqrt(length(.x$absvars)))
) %>%
filter(New_Description != "Spahr 2007") %>%
ungroup() %>%
mutate(
yi = mean_abs_var,
vi = se_abs_var^2)
res <- rma(yi, vi, data=dat)
res ##
## Random-Effects Model (k = 21; tau^2 estimator: REML)
##
## tau^2 (estimated amount of total heterogeneity): 0.0001 (SE = 0.0001)
## tau (square root of estimated tau^2 value): 0.0107
## I^2 (total heterogeneity / total variability): 60.82%
## H^2 (total variability / sampling variability): 2.55
##
## Test for Heterogeneity:
## Q(df = 20) = 60.4345, p-val < .0001
##
## Model Results:
##
## estimate se zval pval ci.lb ci.ub
## 0.0628 0.0033 18.8998 <.0001 0.0563 0.0694 ***
##
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1Figures together
SDD_together <- cowplot::plot_grid(SDDs, SDDms, ncol = 2,
labels = c("B", "C"),
label_size = 30)
SDD_together
Alternatively, all in a row
ICCs_row <- ICCs + guides(colour=FALSE, shape=FALSE)
forest_legend <- get_legend(ICCs +
theme(legend.position="bottom") +
scale_shape_discrete("Patients:") +
scale_colour_manual("Catheter:",
values=c("black", "red")))
forest_row_legendless <- plot_grid(ICCs_row, SDDs, SDDms,
nrow=1, labels=c("A", "B", "C"),
label_size=30)
forest_row <- plot_grid(forest_row_legendless, forest_legend,
nrow=2, rel_heights = c(15,1))
forest_row
ggsave(forest_row, filename = "figures/forest_three_row.png", width = 16, height = 8)Just ICC and SDD
forest_row2_legendless <- plot_grid(ICCs_row, SDDs,
nrow=1, labels=c("A", "B"),
label_size=30)
forest_row2 <- plot_grid(forest_row2_legendless, forest_legend,
nrow=2, rel_heights = c(15,1))
forest_row2
Are they different
To test the difference between the groups, we’ll bootstrap the difference. That means we take 1000 random samples from each group of the same size with replacement, and calculate the difference to get the null distribution. Then we compare the difference we see to the bootstrap distribution.
trt_compare <- trt_tidy %>%
filter(Description != "Spahr. Octreotide") %>%
select(-Study) %>%
rename(Study= New_Description) %>%
left_join(trt_studydemog) %>%
mutate(decomp = ifelse(Perc_Decomp >0 ,
yes="Includes Decompensated",
no = "Only Compensated")) %>%
group_by(decomp) %>%
nest()ICC
bootstrap_icc_single <- function(data) {
sample_ids <- unique(data$`Serial number`)
ids <- sample(sample_ids, length(sample_ids), replace=TRUE)
data_nested <- data %>%
select(`Serial number`, MEASUREMENT, PP) %>%
nest_by(`Serial number`)
boot_sample <- tibble(
`Serial number` = ids
) %>%
left_join(data_nested, by="Serial number") %>%
select(-`Serial number`) %>%
mutate(boot_serial = 1:n()) %>%
unnest(data) %>%
relfeas::trt_widify("PP", "boot_serial", "MEASUREMENT")
boot_icc <- suppressMessages(
suppressWarnings(
psych::ICC(boot_sample[,c(2,3)])$results$ICC[2] ) )
return(boot_icc)
}
bootstrap_icc <- function(n, data, colname=NULL) {
out <- tibble(
n = 1:n
) %>%
mutate(boot_icc = map_dbl(n, ~bootstrap_icc_single(data)))
if(!is.null(colname)) {
colnames(out)[2] <- colname
}
return(out)
}trt_compare_iccvals <- trt_compare %>%
mutate(boot = map2(data, decomp, ~bootstrap_icc(10000, .x))) %>%
select(-data) %>%
unnest(boot)trt_compare_icc <- trt_compare_iccvals %>%
spread(decomp, boot_icc) %>%
mutate(dif = `Only Compensated` - `Includes Decompensated`)
quantile(trt_compare_icc$dif, c(0.025, 0.5, 0.975)) # 95% CI## 2.5% 50% 97.5%
## -0.09604300 -0.01736313 0.066491281-sum(trt_compare_icc$dif > 0)/10000 # one-sided p value## [1] 0.6645Not significant
SDD
bootstrap_sdd_single <- function(data) {
sample_ids <- unique(data$`Serial number`)
ids <- sample(sample_ids, length(sample_ids), replace=TRUE)
data_nested <- data %>%
select(`Serial number`, MEASUREMENT, PP) %>%
nest_by(`Serial number`)
boot_sample <- tibble(
`Serial number` = ids
) %>%
left_join(data_nested, by="Serial number") %>%
select(-`Serial number`) %>%
mutate(boot_serial = 1:n()) %>%
unnest(data) %>%
relfeas::trt_widify("PP", "boot_serial", "MEASUREMENT")
boot_sdd <- suppressMessages(
suppressWarnings(
agRee::agree.sdd(as.matrix(boot_sample[,c(2,3)]))$value ) )
return(boot_sdd)
}
bootstrap_sdd_single <- function(data) {
sample_ids <- unique(data$`Serial number`)
ids <- sample(sample_ids, length(sample_ids), replace=TRUE)
data_nested <- data %>%
select(`Serial number`, MEASUREMENT, PP) %>%
nest_by(`Serial number`)
boot_sample <- tibble(
`Serial number` = ids
) %>%
left_join(data_nested, by="Serial number") %>%
select(-`Serial number`) %>%
mutate(boot_serial = 1:n()) %>%
unnest(data) %>%
relfeas::trt_widify("PP", "boot_serial", "MEASUREMENT")
boot_sdd <- suppressMessages(
suppressWarnings(
agRee::agree.sdd(as.matrix(boot_sample[,c(2,3)]))$value ) )
return(boot_sdd)
}
bootstrap_sdd <- function(n, data, colname=NULL) {
out <- tibble(
n = 1:n
) %>%
mutate(boot_sdd = map_dbl(n, ~bootstrap_sdd_single(data)))
if(!is.null(colname)) {
colnames(out)[2] <- colname
}
return(out)
}
# bootstrap_sdd_single(trt_compare$data[[1]])
# bootstrap_sdd(100, trt_compare$data[[1]], "test")And now we test
trt_compare_sddvals <- trt_compare %>%
mutate(boot = map2(data, decomp, ~bootstrap_sdd(10000, .x))) %>%
select(-data) %>%
unnest(boot)trt_compare_sdd <- trt_compare_sddvals %>%
spread(decomp, boot_sdd) %>%
mutate(dif = `Includes Decompensated` - `Only Compensated`)
quantile(trt_compare_sdd$dif, c(0.025, 0.5, 0.975)) # 95% CI## 2.5% 50% 97.5%
## -0.2412147 0.8292606 2.04805281-sum(trt_compare_sdd$dif > 0)/10000 # one-sided p value## [1] 0.0678SDDM
Percentage SDD
bootstrap_sddm_single <- function(data) {
sample_ids <- unique(data$`Serial number`)
ids <- sample(sample_ids, length(sample_ids), replace=TRUE)
data_nested <- data %>%
select(`Serial number`, MEASUREMENT, PP) %>%
nest_by(`Serial number`)
boot_sample <- tibble(
`Serial number` = ids
) %>%
left_join(data_nested, by="Serial number") %>%
select(-`Serial number`) %>%
mutate(boot_serial = 1:n()) %>%
unnest(data) %>%
relfeas::trt_widify("PP", "boot_serial", "MEASUREMENT")
boot_sddm <- suppressMessages(
suppressWarnings(
agRee::agree.sddm(as.matrix(boot_sample[,c(2,3)]))$value ) )
return(boot_sddm)
}
bootstrap_sddm <- function(n, data, colname=NULL) {
out <- tibble(
n = 1:n
) %>%
mutate(boot_sddm = map_dbl(n, ~bootstrap_sddm_single(data)))
if(!is.null(colname)) {
colnames(out)[2] <- colname
}
return(out)
}
# bootstrap_sddm_single(trt_compare$data[[1]])
# bootstrap_sddm(100, trt_compare$data[[1]], "test")And now we test
trt_compare_sddmvals <- trt_compare %>%
mutate(boot = map2(data, decomp, ~bootstrap_sddm(10000, .x))) %>%
select(-data) %>%
unnest(boot)trt_compare_sddm <- trt_compare_sddmvals %>%
spread(decomp, boot_sddm) %>%
mutate(dif = `Includes Decompensated` - `Only Compensated`)
quantile(trt_compare_sddm$dif, c(0.025, 0.5, 0.975)) # 95% CI## 2.5% 50% 97.5%
## -0.03102582 0.03489179 0.105832681-sum(trt_compare_sddm$dif > 0)/10000 # one-sided p value## [1] 0.1557Causes of differences
Here, we perform an exploratory analysis of which factors may contribute to differences
trt_wide <- trt_tidy %>%
select(-Study) %>%
rename(Study= New_Description) %>%
spread(MEASUREMENT, PP) %>%
rename(Meas1 = `1`,
Meas2 = `2`) %>%
mutate(change = Meas2 - Meas1,
abschange=abs(change),
meanval = (Meas1 + Meas2)/2) %>%
left_join(studynames) %>%
left_join(trt_studydemog) %>%
mutate(Description = as.factor(Description)) %>%
filter(Description != "Spahr. Octreotide") %>%
mutate(decomp = ifelse(Perc_Decomp == 0,
"Only Compensated",
"Includes Decompensated"))
trt_wide_c <- trt_wide %>%
filter(Perc_Decomp == 0)
trt_wide_dc <- trt_wide %>%
filter(Perc_Decomp > 0)Skewness
Absolute
Let’s just visualise our distribution.
ggplot(trt_wide, aes(x=abschange)) +
geom_density(fill="black",alpha=0.5)
And between groups
ggplot(trt_wide, aes(x=abschange)) +
geom_density(aes(colour=decomp, fill=decomp),alpha=0.5) +
facet_wrap(decomp~., nrow=2) +
theme(legend.position="bottom")
And let’s get some values for that too
psych::describe(trt_wide$abschange)psych::describeBy(trt_wide$abschange, group=trt_wide$decomp)##
## Descriptive statistics by group
## group: Includes Decompensated
## vars n mean sd median trimmed mad min max range skew kurtosis se
## X1 1 166 1.79 1.94 1 1.46 1.11 0 13.5 13.5 2.45 8.89 0.15
## --------------------------------------------------------------------------------------------------------------------------------------------------
## group: Only Compensated
## vars n mean sd median trimmed mad min max range skew kurtosis se
## X1 1 115 1.67 1.42 1 1.56 1.48 0 6 6 0.57 -0.64 0.13Signed
Let’s just visualise our overall distribution.
ggplot(trt_wide, aes(x=change)) +
geom_density(fill="black",alpha=0.5)
… and by group
ggplot(trt_wide, aes(x=change)) +
geom_density(aes(colour=decomp, fill=decomp),alpha=0.5) +
facet_wrap(decomp~., nrow=2) +
theme(legend.position="bottom")
For signed differences, let’s assess whether they differ from zero.
summary(lmer(change ~ 1 + (1|Study), data=trt_wide))## Linear mixed model fit by REML. t-tests use Satterthwaite's method ['lmerModLmerTest']
## Formula: change ~ 1 + (1 | Study)
## Data: trt_wide
##
## REML criterion at convergence: 1304.2
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -5.1470 -0.4712 -0.0170 0.5292 3.7968
##
## Random effects:
## Groups Name Variance Std.Dev.
## Study (Intercept) 0.2793 0.5285
## Residual 5.8542 2.4195
## Number of obs: 281, groups: Study, 21
##
## Fixed effects:
## Estimate Std. Error df t value Pr(>|t|)
## (Intercept) -0.03655 0.19379 9.51195 -0.189 0.854summary(lmer(change ~ 1 + (1|Study), data=trt_wide_c))## Linear mixed model fit by REML. t-tests use Satterthwaite's method ['lmerModLmerTest']
## Formula: change ~ 1 + (1 | Study)
## Data: trt_wide_c
##
## REML criterion at convergence: 506.5
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -2.1852 -0.5692 -0.1075 0.7360 2.6627
##
## Random effects:
## Groups Name Variance Std.Dev.
## Study (Intercept) 0.1414 0.3761
## Residual 4.6911 2.1659
## Number of obs: 115, groups: Study, 7
##
## Fixed effects:
## Estimate Std. Error df t value Pr(>|t|)
## (Intercept) 0.2522 0.2659 3.4807 0.948 0.404summary(lmer(change ~ 1 + (1|Study), data=trt_wide_dc))## Linear mixed model fit by REML. t-tests use Satterthwaite's method ['lmerModLmerTest']
## Formula: change ~ 1 + (1 | Study)
## Data: trt_wide_dc
##
## REML criterion at convergence: 792
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -4.7455 -0.4164 0.0247 0.4964 3.5999
##
## Random effects:
## Groups Name Variance Std.Dev.
## Study (Intercept) 0.3612 0.601
## Residual 6.6449 2.578
## Number of obs: 166, groups: Study, 14
##
## Fixed effects:
## Estimate Std. Error df t value Pr(>|t|)
## (Intercept) -0.200 0.263 5.868 -0.76 0.476Not significantly different from zero in either the combined sample or each group.
And some values
psych::describe(trt_wide$change)psych::describeBy(trt_wide$change, group=trt_wide$decomp)##
## Descriptive statistics by group
## group: Includes Decompensated
## vars n mean sd median trimmed mad min max range skew kurtosis se
## X1 1 166 -0.2 2.63 0 -0.1 1.48 -13.5 9 22.5 -0.75 4.57 0.2
## --------------------------------------------------------------------------------------------------------------------------------------------------
## group: Only Compensated
## vars n mean sd median trimmed mad min max range skew kurtosis se
## X1 1 115 0.22 2.19 0 0.22 1.48 -4.5 6 10.5 0.08 -0.4 0.2Figures
Let’s make some combined figures for the paper
sign_change_distr <- trt_wide %>%
mutate(decomp = as.factor(decomp)) %>%
ggplot(aes(x=change, colour=decomp, fill=decomp, group=decomp)) +
geom_density(aes(colour=decomp, fill=decomp),alpha=0.5) +
theme(legend.position=c(0.3, 0.9)) +
scale_color_brewer("Patients", type = "qual", palette = 1) +
scale_fill_brewer("Patients", type = "qual", palette = 1) +
guides(fill=FALSE) +
labs(y = "",
x = "Signed Change from first to second measurement (mmHg)") +
theme(axis.text.y = element_blank(),
axis.ticks.y=element_blank())
sign_change_distr
abs_change_distr <- trt_wide %>%
mutate(decomp = as.factor(decomp)) %>%
ggplot(aes(x=abschange, colour=decomp, fill=decomp, group=decomp)) +
geom_density(aes(colour=decomp, fill=decomp),alpha=0.5) +
theme(legend.position=c(0.5, 0.9)) +
scale_color_brewer("Patients", type = "qual", palette = 1) +
scale_fill_brewer("Patients", type = "qual", palette = 1) +
guides(fill=FALSE) +
labs(y = "",
x = "Absolute Change from first to second measurement (mmHg)") +
theme(axis.text.y = element_blank(),
axis.ticks.y=element_blank())
abs_change_distr
Percentage Decomp
permTREND(formula=abschange ~ Perc_Decomp, data=trt_wide,
method="exact.mc")##
## Exact Permutation Test Estimated by Monte Carlo
##
## data: x and y
## p-value = 0.032
## alternative hypothesis: true correlation of x and y is not equal to 0
## sample estimates:
## correlation of x and y
## 0.1262568
##
## p-value estimated from 999 Monte Carlo replications
## 99 percent confidence interval on p-value:
## 0.01384991 0.05601331permuco::lmperm(abschange ~ Perc_Decomp, data=trt_wide)## Table of marginal t-test of the betas
## Permutation test using freedman_lane to handle nuisance variables and 5000 permutations.
## Estimate Std. Error t value parametric Pr(>|t|) permutation Pr(<t) permutation Pr(>t) permutation Pr(>|t|)
## (Intercept) 1.499246 0.153912 9.741 1.725e-19
## Perc_Decomp 0.005031 0.002367 2.126 3.439e-02 0.9812 0.019 0.0362decomp_plot <- ggplot(trt_wide, aes(x=Perc_Decomp, y=abschange)) +
geom_beeswarm(aes(colour=as.factor(Study),
group=as.factor(Perc_Decomp)),
alpha=0.4, cex=1) +
guides(colour=FALSE) +
geom_smooth(method="lm", se = FALSE) +
labs(x="Decompensated Patients (%)",
y="Absolute Change (mmHg)")
decomp_plot
Days elapsed
permuco::lmperm(abschange ~ Days + Perc_Decomp, data=trt_wide)## Table of marginal t-test of the betas
## Permutation test using freedman_lane to handle nuisance variables and 5000 permutations.
## Estimate Std. Error t value parametric Pr(>|t|) permutation Pr(<t) permutation Pr(>t) permutation Pr(>|t|)
## (Intercept) 1.6031874 0.1994382 8.0385 2.624e-14
## Days -0.0006133 0.0007477 -0.8202 4.128e-01 0.2076 0.7926 0.3990
## Perc_Decomp 0.0041622 0.0025941 1.6045 1.097e-01 0.9524 0.0478 0.1026Now let’s plot, after correcting for the effect of the patient groups.
correct_for_decomp <- function(formula) {
formula <- as.formula(formula)
coefficients <- coef(permuco::lmperm(formula,
data=trt_wide))
predicted <- as.character(formula[2])
after_decomp_corr <- trt_wide[[predicted]] -
trt_wide[["Perc_Decomp"]] * coefficients[which(names(coefficients)=="Perc_Decomp")]
return(after_decomp_corr)
}
days_plot <- trt_wide %>%
mutate(abschange_dccorr = correct_for_decomp(abschange ~ Days + Perc_Decomp)) %>%
ggplot(aes(x=Days, y=abschange_dccorr)) +
geom_beeswarm(aes(colour=Study, group=Study), alpha=0.4, cex=1) +
guides(colour=FALSE) +
geom_smooth(method="lm", se=FALSE) +
labs(y="Absolute Change (mmHg)\n(after correction for Decompensated Percentage)",
x="Days Elapsed between Measurements")
days_plot
Percentage Alcoholic
permuco::lmperm(abschange ~ Perc_Alc + Perc_Decomp, data=trt_wide)## Table of marginal t-test of the betas
## Permutation test using freedman_lane to handle nuisance variables and 5000 permutations.
## Estimate Std. Error t value parametric Pr(>|t|) permutation Pr(<t) permutation Pr(>t) permutation Pr(>|t|)
## (Intercept) 1.94758 0.166155 11.721 4.711e-26
## Perc_Alc -0.02579 0.004560 -5.655 3.869e-08 2e-04 1e+00 2e-04
## Perc_Decomp 0.01881 0.003313 5.677 3.447e-08 1e+00 2e-04 2e-04permTREND(formula=abschange ~ Perc_Alc, data=trt_wide_c,
method="exact.mc")##
## Exact Permutation Test Estimated by Monte Carlo
##
## data: x and y
## p-value = 0.01
## alternative hypothesis: true correlation of x and y is not equal to 0
## sample estimates:
## correlation of x and y
## -0.2373197
##
## p-value estimated from 999 Monte Carlo replications
## 99 percent confidence interval on p-value:
## 0.001347329 0.025105152permTREND(formula=abschange ~ Perc_Alc, data=trt_wide_dc,
method="exact.mc")##
## Exact Permutation Test Estimated by Monte Carlo
##
## data: x and y
## p-value = 0.006
## alternative hypothesis: true correlation of x and y is not equal to 0
## sample estimates:
## correlation of x and y
## -0.2099865
##
## p-value estimated from 999 Monte Carlo replications
## 99 percent confidence interval on p-value:
## 0.0002072893 0.0184986927perc_alc_plot <- trt_wide %>%
mutate(abschange_dccorr = correct_for_decomp(abschange ~ Perc_Alc + Perc_Decomp)) %>%
ggplot(aes(x=Perc_Alc, y=abschange_dccorr)) +
geom_beeswarm(aes(colour=Study, group=Study), alpha=0.4, cex=1) +
guides(colour=FALSE) +
geom_smooth(method="lm", se=FALSE) +
labs(y="Absolute Change (mmHg)\n(after correction for Decompensated Percentage)",
x="Percentage of Alcoholic Patients (%)")
perc_alc_plot
Multicentre
permuco::lmperm(abschange ~ Centre + Perc_Decomp, data=trt_wide)## Table of marginal t-test of the betas
## Permutation test using freedman_lane to handle nuisance variables and 5000 permutations.
## Estimate Std. Error t value parametric Pr(>|t|) permutation Pr(<t) permutation Pr(>t) permutation Pr(>|t|)
## (Intercept) 1.663139 0.165791 10.032 2.056e-20
## CentreSingle-centre -0.544349 0.216320 -2.516 1.242e-02 0.0062 0.994 0.0136
## Perc_Decomp 0.007055 0.002478 2.846 4.750e-03 0.9982 0.002 0.0040centre_plot <- trt_wide %>%
mutate(abschange_dccorr = correct_for_decomp(abschange ~ Centre + Perc_Decomp)) %>%
ggplot(aes(x=Centre, y=abschange_dccorr)) +
geom_beeswarm(aes(colour=Study, group=Study), alpha=0.4, cex=1) +
guides(colour=FALSE) +
geom_smooth(method="lm", se=FALSE) +
labs(y="Absolute Change (mmHg)\n(after correction for Decompensated Percentage)")
centre_plot
Combined Model
permuco::lmperm(abschange ~ Perc_Decomp + Centre + Perc_Alc, data=trt_wide)## Table of marginal t-test of the betas
## Permutation test using freedman_lane to handle nuisance variables and 5000 permutations.
## Estimate Std. Error t value parametric Pr(>|t|) permutation Pr(<t) permutation Pr(>t) permutation Pr(>|t|)
## (Intercept) 1.94534 0.168789 11.52527 2.287e-25
## Perc_Decomp 0.01884 0.003349 5.62673 4.493e-08 1.0000 0.0002 0.0002
## CentreSingle-centre 0.01892 0.236163 0.08012 9.362e-01 0.5338 0.4664 0.9270
## Perc_Alc -0.02599 0.005198 -4.99906 1.023e-06 0.0002 1.0000 0.0002permuco::lmperm(abschange ~ Centre + Perc_Alc, data=trt_wide_c)## Table of marginal t-test of the betas
## Permutation test using freedman_lane to handle nuisance variables and 5000 permutations.
## Estimate Std. Error t value parametric Pr(>|t|) permutation Pr(<t) permutation Pr(>t) permutation Pr(>|t|)
## (Intercept) 1.99513 0.170383 11.710 3.636e-21
## CentreSingle-centre -0.38265 0.310236 -1.233 2.200e-01 0.1070 0.8932 0.2218
## Perc_Alc -0.01289 0.007501 -1.718 8.858e-02 0.0474 0.9528 0.0924permuco::lmperm(abschange ~ Centre + Perc_Alc, data=trt_wide_dc)## Table of marginal t-test of the betas
## Permutation test using freedman_lane to handle nuisance variables and 5000 permutations.
## Estimate Std. Error t value parametric Pr(>|t|) permutation Pr(<t) permutation Pr(>t) permutation Pr(>|t|)
## (Intercept) 2.99299 0.440666 6.792 1.967e-10
## CentreSingle-centre 0.37572 0.372646 1.008 3.148e-01 0.8450 0.1552 0.3112
## Perc_Alc -0.02274 0.008097 -2.808 5.587e-03 0.0066 0.9936 0.0078Let’s examine why this might be.
trt_wide %>%
ggplot(aes(y=Perc_Decomp, x=Centre)) +
geom_violin()
permTS(formula=Perc_Decomp ~ as.factor(Centre), data=trt_wide,
method="exact.mc")##
## Exact Permutation Test Estimated by Monte Carlo
##
## data: Perc_Decomp by as.factor(Centre)
## p-value = 0.002
## alternative hypothesis: true mean as.factor(Centre)=Multi-centre - mean as.factor(Centre)=Single-centre is not equal to 0
## sample estimates:
## mean as.factor(Centre)=Multi-centre - mean as.factor(Centre)=Single-centre
## -28.31913
##
## p-value estimated from 999 Monte Carlo replications
## 99 percent confidence interval on p-value:
## 0.00000000 0.01057916Most of the single-centre studies have high proportions of decompensated patients.
trt_wide %>%
ggplot(aes(y=Perc_Alc, x=Centre)) +
geom_violin()
permTS(formula=Perc_Alc ~ as.factor(Centre), data=trt_wide,
method="exact.mc")##
## Exact Permutation Test Estimated by Monte Carlo
##
## data: Perc_Alc by as.factor(Centre)
## p-value = 0.002
## alternative hypothesis: true mean as.factor(Centre)=Multi-centre - mean as.factor(Centre)=Single-centre is not equal to 0
## sample estimates:
## mean as.factor(Centre)=Multi-centre - mean as.factor(Centre)=Single-centre
## -34.52329
##
## p-value estimated from 999 Monte Carlo replications
## 99 percent confidence interval on p-value:
## 0.00000000 0.01057916Similarly, most of the single-centre studies have high proportions of alcoholic patients.
Days
Reviewers were surprised at the lack of an effect of the number of days elapsed. Perhaps this was obscured by not having included the other confounding factors.
permuco::lmperm(abschange ~ Perc_Decomp + Centre + Perc_Alc + Days, data=trt_wide)## Table of marginal t-test of the betas
## Permutation test using freedman_lane to handle nuisance variables and 5000 permutations.
## Estimate Std. Error t value parametric Pr(>|t|) permutation Pr(<t) permutation Pr(>t) permutation Pr(>|t|)
## (Intercept) 2.0833441 0.2090856 9.96407 3.545e-20
## Perc_Decomp 0.0178489 0.0034640 5.15263 4.898e-07 1.0000 0.0002 0.0002
## CentreSingle-centre 0.0234628 0.2360917 0.09938 9.209e-01 0.5348 0.4654 0.9186
## Perc_Alc -0.0262613 0.0052018 -5.04852 8.097e-07 0.0002 1.0000 0.0002
## Days -0.0007942 0.0007107 -1.11745 2.648e-01 0.1308 0.8694 0.2550This does not appear to be the case!
Mean Value
Absolute
permuco::lmperm(abschange ~ meanval + Perc_Decomp, data=trt_wide)## Table of marginal t-test of the betas
## Permutation test using freedman_lane to handle nuisance variables and 5000 permutations.
## Estimate Std. Error t value parametric Pr(>|t|) permutation Pr(<t) permutation Pr(>t) permutation Pr(>|t|)
## (Intercept) 1.085870 0.422931 2.567 0.01077
## meanval 0.025623 0.024418 1.049 0.29494 0.8470 0.1532 0.299
## Perc_Decomp 0.004602 0.002401 1.917 0.05630 0.9774 0.0228 0.054permTREND(formula=abschange ~ meanval, data=trt_wide_c,
method="exact.mc")##
## Exact Permutation Test Estimated by Monte Carlo
##
## data: x and y
## p-value = 0.654
## alternative hypothesis: true correlation of x and y is not equal to 0
## sample estimates:
## correlation of x and y
## -0.04578405
##
## p-value estimated from 999 Monte Carlo replications
## 99 percent confidence interval on p-value:
## 0.5770505 0.7316143permTREND(formula=abschange ~ meanval, data=trt_wide_dc,
method="exact.mc")##
## Exact Permutation Test Estimated by Monte Carlo
##
## data: x and y
## p-value = 0.114
## alternative hypothesis: true correlation of x and y is not equal to 0
## sample estimates:
## correlation of x and y
## 0.1302787
##
## p-value estimated from 999 Monte Carlo replications
## 99 percent confidence interval on p-value:
## 0.07792884 0.15503144meanv_abs_plot <- trt_wide %>%
mutate(abschange_dccorr = correct_for_decomp(abschange ~ meanval + Perc_Decomp)) %>%
ggplot(aes(x=meanval, y=abschange_dccorr)) +
geom_point(aes(colour=Study, group=Study), alpha=0.4) +
guides(colour=FALSE) +
geom_smooth(method="lm", se=FALSE) +
labs(y="Absolute Change (mmHg)\n(after correction for Decompensated Percentage)",
x="Mean Value across Measurements (mmHg)")
meanv_abs_plot
Signed
meanv_sign <- lmer(change ~ meanval + Perc_Decomp + (1 | Study), data = trt_wide)
summary(meanv_sign)## Linear mixed model fit by REML. t-tests use Satterthwaite's method ['lmerModLmerTest']
## Formula: change ~ meanval + Perc_Decomp + (1 | Study)
## Data: trt_wide
##
## REML criterion at convergence: 1304
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -4.8083 -0.6359 0.0657 0.5932 3.9860
##
## Random effects:
## Groups Name Variance Std.Dev.
## Study (Intercept) 0.4263 0.6529
## Residual 5.5354 2.3527
## Number of obs: 281, groups: Study, 21
##
## Fixed effects:
## Estimate Std. Error df t value Pr(>|t|)
## (Intercept) -1.773365 0.658135 70.196412 -2.695 0.008813 **
## meanval 0.125777 0.034937 258.265538 3.600 0.000381 ***
## Perc_Decomp -0.007595 0.004939 10.005645 -1.538 0.155110
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Correlation of Fixed Effects:
## (Intr) meanvl
## meanval -0.860
## Perc_Decomp -0.301 -0.110meanv_sign_nocorr <- lmer(change ~ meanval + (1 | Study), data = trt_wide)
summary(meanv_sign_nocorr)## Linear mixed model fit by REML. t-tests use Satterthwaite's method ['lmerModLmerTest']
## Formula: change ~ meanval + (1 | Study)
## Data: trt_wide
##
## REML criterion at convergence: 1297.6
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -4.8493 -0.6062 0.0470 0.5689 3.9289
##
## Random effects:
## Groups Name Variance Std.Dev.
## Study (Intercept) 0.505 0.7106
## Residual 5.530 2.3515
## Number of obs: 281, groups: Study, 21
##
## Fixed effects:
## Estimate Std. Error df t value Pr(>|t|)
## (Intercept) -2.1062 0.6338 161.0550 -3.323 0.001102 **
## meanval 0.1215 0.0349 258.7515 3.481 0.000586 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Correlation of Fixed Effects:
## (Intr)
## meanval -0.938meanv_sign_c <- lmer(change ~ meanval + (1 | Study), data = trt_wide_c)
summary(meanv_sign_c)## Linear mixed model fit by REML. t-tests use Satterthwaite's method ['lmerModLmerTest']
## Formula: change ~ meanval + (1 | Study)
## Data: trt_wide_c
##
## REML criterion at convergence: 505.3
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -1.95680 -0.66000 -0.09292 0.72674 2.50831
##
## Random effects:
## Groups Name Variance Std.Dev.
## Study (Intercept) 0.1447 0.3804
## Residual 4.5220 2.1265
## Number of obs: 115, groups: Study, 7
##
## Fixed effects:
## Estimate Std. Error df t value Pr(>|t|)
## (Intercept) -1.82528 0.95247 64.26834 -1.916 0.0598 .
## meanval 0.12622 0.05556 102.76959 2.272 0.0252 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Correlation of Fixed Effects:
## (Intr)
## meanval -0.961meanv_sign_dc <- lmer(change ~ meanval + (1 | Study), data = trt_wide_dc)
summary(meanv_sign_dc)## Linear mixed model fit by REML. t-tests use Satterthwaite's method ['lmerModLmerTest']
## Formula: change ~ meanval + (1 | Study)
## Data: trt_wide_dc
##
## REML criterion at convergence: 789.3
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -4.4469 -0.5597 0.1251 0.5181 3.7263
##
## Random effects:
## Groups Name Variance Std.Dev.
## Study (Intercept) 0.6818 0.8257
## Residual 6.2470 2.4994
## Number of obs: 166, groups: Study, 14
##
## Fixed effects:
## Estimate Std. Error df t value Pr(>|t|)
## (Intercept) -2.33529 0.83332 100.93794 -2.802 0.00608 **
## meanval 0.12351 0.04499 153.92550 2.745 0.00677 **
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Correlation of Fixed Effects:
## (Intr)
## meanval -0.932correct_for_decomp_lmer <- function(formula) {
formula <- as.formula(formula)
coefficients <- fixef(lmer(formula, data=trt_wide))
predicted <- as.character(formula[2])
after_decomp_corr <- trt_wide[[predicted]] -
trt_wide[["Perc_Decomp"]] * coefficients[which(names(coefficients)=="Perc_Decomp")]
return(after_decomp_corr)
}
meanv_signed_plot <- trt_wide %>%
mutate(change_dccorr = correct_for_decomp_lmer("change ~ meanval + Perc_Decomp + (1 | Study)")) %>%
ggplot(aes(x=meanval, y=change_dccorr)) +
geom_jitter(aes(colour=Study, group=Study), alpha=0.4, height = 0.2) +
guides(colour=FALSE) +
geom_smooth(method="lm", se=FALSE) +
labs(y="Signed Change (mmHg)\n(after correction for Decompensated Percentage)",
x="Mean Value across Measurements (mmHg)")
meanv_signed_plot
meanv_signed_plot_nocorr <- ggplot(data=trt_wide, aes(x=meanval, y=change)) +
geom_jitter(aes(colour=Study, group=Study), alpha=0.4, height = 0.2) +
guides(colour=FALSE) +
geom_smooth(method="lm", se=FALSE) +
labs(y="Signed Change (mmHg)\n(jittered slightly to avoid overlap)",
x="Mean Value across Measurements (mmHg)")
meanv_signed_plot_nocorr
Figures
cowplot::plot_grid(decomp_plot, days_plot,
perc_alc_plot, centre_plot, align = "hv",
ncol = 2, labels = "AUTO")
cowplot::plot_grid(abs_change_distr, sign_change_distr,
meanv_abs_plot, meanv_signed_plot,
align = "hv",
ncol = 2, labels = "AUTO")
Power Analysis for a difference
Now, the core thing we want to do here is to perform a power analysis for examining within-individual effects.
One way of doing this is to use the signvar_sd column of the tidytrt object. This is the standard deviation of the signed changes, and hence, if we assume a change after an intervention, this is the SD we could imagine being true, and thus, the effect size, the Cohen’s Dz, is equal to difference / signvar_sd. However, this method makes an assumption that everyone changes by exactly the same amount: the effect (before accounting for error) is completely uniform. This may be the case, but this is the most optimistic scenario. We should be taking into consideration the possibility of heterogeneous effects.
First, let’s make a little plot to show what I mean by homogeneous and heterogeneous effects.
set.seed(1234)
trt_all_comp <- trt_all[2,]
wscv=trt_all_comp$wscv
meanval=trt_all_comp$mean
cv=trt_all_comp$cv
icc=trt_all_comp$icc
sd_true <- sqrt(icc * (cv * meanval)^2)
n <- 20
delta <- 2
# Homogeneous
cv_delta <- 0
pre_true <- rnorm(n, meanval, sd_true)
pre_meas <- pre_true + rnorm(n, 0, meanval*wscv)
post_true <- pre_true - rnorm(n, delta, cv_delta*delta)
post_meas <- post_true + rnorm(n, 0, meanval*wscv)
hom_true <- tibble::tibble(
ID = rep(1:n, times=2),
Outcome = c(pre_true, post_true),
PrePost = rep(c("Pre", "Post"), each=n),
Effects = "Homogeneous Effects",
MeasuredTrue = "True Values"
)
hom_measured <- tibble::tibble(
ID = rep(1:n, times=2),
Outcome = c(pre_meas, post_meas),
PrePost = rep(c("Pre", "Post"), each=n),
Effects = "Homogeneous Effects",
MeasuredTrue = "Measured Values"
)
# hom_difference <- tibble::tibble(
# ID = rep(1:n, times=2),
# Outcome = c(post_meas-pre_),
# PrePost = rep(c("Pre", "Post"), each=n),
# Effects = "Homogeneous",
# MeasuredTrue = "Difference"
# )
# Heterogeneous
cv_delta <- 0.5
#pre_true <- rnorm(n, meanval, abs(cv*meanval)) # Use same as above
#pre_meas <- pre_true + rnorm(n, 0, abs(meanval*wscv))
post_true <- pre_true - rnorm(n, delta, abs(cv_delta*delta))
post_meas <- post_true + rnorm(n, 0, abs(meanval*wscv))
het_true <- tibble::tibble(
ID = rep(1:n, times=2),
Outcome = c(pre_true, post_true),
PrePost = rep(c("Pre", "Post"), each=n),
Effects = "Heterogeneous Effects",
MeasuredTrue = "True Values"
)
het_measured <- tibble::tibble(
ID = rep(1:n, times=2),
Outcome = c(pre_meas, post_meas),
PrePost = rep(c("Pre", "Post"), each=n),
Effects = "Heterogeneous Effects",
MeasuredTrue = "Measured Values"
)
# Plot
effects <- bind_rows(hom_true, hom_measured, het_true, het_measured) %>%
mutate(MeasuredTrue = fct_inorder(MeasuredTrue),
Effects = fct_inorder(Effects),
PrePost = fct_inorder(PrePost),
ID = as.factor(ID))
ggplot(effects, aes(x=PrePost, y=Outcome, colour=ID, group=ID)) +
geom_point(size=2) +
geom_line() +
facet_grid(Effects~MeasuredTrue) +
labs(y="Outcome (mmHg)",
colour="Values",
x=NULL,
title="Homogeneous and Heteregeneous Effects",
subtitle="Homogeneous effects imply that the true underlying change is the same\nin all individuals (hence parallel lines in the true values)") +
guides(colour=FALSE)
So, to summarise, we have underlying true values, and measured values after accounting for measurement error. The change from before to after the intervention can either be homogeneous (everyone has exactly the same effect), or heterogeneous (effect sizes differ, and some even get harmed by the intervention - about 2.5% as I’ve chosen the SD of the intervention effect as 50% of the mean effect, so 0 effect is 2 SDs away from the mean effect size, which is approximately 2.5%). Then, the measured values appear to show more people getting worse after treatment, but this is just due to measurement error.
heterogen_cv <- 0.5
annotations <- tibble(
x=c(-3, 0),
text=c(paste0(round(100*pnorm(1/heterogen_cv)), "% experience improvements"),
paste0(100-round(100*pnorm(1/heterogen_cv)), "% experience worsening")),
colour = c("#61b096", "#bd7969")
)
heterogen_effects <- tibble(Effect=c(-3, 1))
ggplot(heterogen_effects, aes(x=Effect)) +
geom_area(stat="function", fun = dnorm, fill="#61b096", xlim=c(-3, 0),
args = list(mean = -1, sd=heterogen_cv), alpha=0.7) +
geom_area(stat="function", fun = dnorm, fill="#bd7969", xlim=c(0, 1),
args = list(mean = -1, sd=heterogen_cv), alpha=0.7) +
annotate("text", x=-2.5, y=0.7,
label=paste0(round(100*pnorm(1/heterogen_cv), 1),
"% experience\nimprovements"),
colour = "#61b096", hjust=0.5) +
annotate("text", x=0.5, y=0.7,
label=paste0(100-round(100*pnorm(1/heterogen_cv), 1),
"% experience\nworsening"),
colour = "#bd7969", hjust=0.5) +
annotate("text", x=-0.8, y=0.2,
label="Mean\neffect",hjust=0.5) +
theme(axis.title.y=element_blank(),
axis.text.y=element_blank(),
axis.ticks.y=element_blank()) +
geom_vline(xintercept = -1) +
labs(title="Heterogeneous Effects",
subtitle=paste0("Using a 50% CV for effect heterogeneity implies that some ",
"participants\nmay benefit more and others may even have ",
"worsening."))
This would imply that for all different sizes of effect, that only 2.3% experience a true worsening. However, when we measure the values, there are also several individuals who will exhibit an apparent worsening (increases from first to second measurement), when their true underlying values exhibited improvements. Let’s calculate what fraction of individuals this would be.
True and Apparent Changes
Here, we can also observe the percentage of individuals who show apparent 10% and 20% changes from baseline.
apparent_effects <- function(n, delta, cv_delta, wscv=trt_all$wscv,
mean=trt_all$mean, cv=trt_all$cv, icc=trt_all$icc,
decomp) {
wscv <- wscv[decomp]
mean <- mean[decomp]
cv <- cv[decomp]
var <- (cv*mean)^2
sd_true <- sqrt(var * icc)
pre_true <- rnorm(n, mean, sd_true)
pre_meas <- pre_true + rnorm(n, 0, mean*wscv)
post_true <- pre_true - rnorm(n, delta, cv_delta*delta)
post_meas <- post_true + rnorm(n, 0, mean*wscv)
measured <- tibble::tibble(
ID = rep(1:n, times=2),
Outcome = c(pre_meas, post_meas),
PrePost = rep(c("Pre", "Post"), each=n)
) %>%
spread(PrePost, Outcome)
true <- tibble::tibble(
ID = rep(1:n, times=2),
Outcome = c(pre_true, post_true),
PrePost = rep(c("Pre", "Post"), each=n)
) %>%
spread(PrePost, Outcome)
out <- list()
out$apparent_worse <- round(100*with(measured, mean(Post > Pre)),1)
out$apparent_10 <- round(100*with(measured, mean((Pre-Post)/Pre > 0.1)),1)
out$apparent_20 <- round(100*with(measured, mean((Pre-Post)/Pre > 0.2)),1)
out$true_worse <- round(100*with(true, mean(Post > Pre)),1)
out$true_10 <- round(100*with(true, mean((Pre-Post)/Pre > 0.1)),1)
out$true_20 <- round(100*with(true, mean((Pre-Post)/Pre > 0.2)),1)
return(out)
}
if(!file.exists("../DerivedData/percdifs.rds") || overwrite) {
measured_percs <- tidyr::crossing(
delta = seq(0, 3, by=0.5),
cv_delta = c(0, 0.5),
decomp=c(1,2)
) %>%
mutate(condition = 1:n()) %>%
group_by(condition) %>%
nest() %>%
mutate(res = map(data, ~apparent_effects( n=1e7,
delta=.x$delta,
cv_delta = .x$cv_delta,
decomp=.x$decomp))) %>%
ungroup()
saveRDS(measured_percs, "../DerivedData/percdifs.rds")
}measured_percs <- readRDS("../DerivedData/percdifs.rds")
measured_percs_summary <- measured_percs %>%
mutate(apparent_worse = map_dbl(res, "apparent_worse"),
apparent_10 = map_dbl(res, "apparent_10"),
apparent_20 = map_dbl(res, "apparent_20"),
true_worse = map_dbl(res, "true_worse"),
true_10 = map_dbl(res, "true_10"),
true_20 = map_dbl(res, "true_20")) %>%
select(-res) %>%
unnest(data) %>%
#mutate(true_worse = round(100*(1-pnorm(1/cv_delta)),1)) %>%
arrange(decomp, delta, cv_delta) %>%
mutate(decomp = ifelse(decomp==1,
trt_all$decomp[1],
trt_all$decomp[2]),
cv_delta = ifelse(cv_delta==0,
"Homogeneous",
"Heterogeneous")) %>%
select(decomp, condition, delta, cv_delta,
true_worse, apparent_worse,
true_10, apparent_10,
true_20, apparent_20) %>%
rename("Patients" = decomp,
"Apparent Worsening (%)" = apparent_worse,
"True Worsening (%)" = true_worse,
"True 10%+ Improvement (%)" = true_10,
"Apparent 10%+ Improvement (%)" = apparent_10,
"True 20%+ Improvement (%)" = true_20,
"Apparent 20%+ Improvement (%)" = apparent_20,
"Effects" = cv_delta,
"Difference" = delta) %>%
select(-condition)
decomp_change <- head(
which(
measured_percs_summary$Patients ==
trt_all$decomp[2]), 1)
knitr::kable(measured_percs_summary[,-1]) %>%
kable_styling("striped", full_width = F) %>%
pack_rows(trt_all$decomp[1], 1, decomp_change-1) %>%
pack_rows(trt_all$decomp[2], decomp_change, nrow(measured_percs_summary))appchange <- knitr::kable(measured_percs_summary[,-1]) %>%
kable_styling("striped", full_width = F) %>%
pack_rows(trt_all$decomp[1], 1, decomp_change-1) %>%
pack_rows(trt_all$decomp[2], decomp_change, nrow(measured_percs_summary))
appchange# save_kable(appchange, file = "figures/appchange.jpg")So, for a true effect of about 2mmHg in compensated patients, it will appear as if 12-16% would appear to worsen. This fits with clinical experience.
Simulation
Note: these are no longer run as we instead make use of the analytical solutions
HVPG_dif_sim <- function(n, delta, cv_delta, wscv=trt_all$wscv,
mean=trt_all$mean, cv=trt_all$cv, icc=trt_all$icc,
decomp = 1) {
wscv <- wscv[decomp]
mean <- mean[decomp]
cv <- cv[decomp]
var <- (cv*mean)^2
sd_true <- sqrt(var * icc)
pre_true <- rnorm(n, mean, sd_true)
pre_meas <- pre_true + rnorm(n, 0, mean*wscv)
post_true <- pre_true - rnorm(n, delta, cv_delta*delta)
post_meas <- post_true + rnorm(n, 0, mean*wscv)
measured <- tibble::tibble(
ID = rep(1:n, times=2),
Outcome = c(pre_meas, post_meas),
PrePost = rep(c("Pre", "Post"), each=n)
)
d <- effsize::cohen.d(measured$Outcome, measured$PrePost,
paired=TRUE)$estimate
dz <- effsize::cohen.d(measured$Outcome, measured$PrePost,
paired=TRUE, within=FALSE)$estimate
test <- t.test(pre_meas, post_meas, alternative = "greater",
paired = T)
# Note: one-sided p value
testout <- broom::tidy(test)
out <- mutate(testout, d = d, dz = dz)
return(out)
}Now, we set up the simulation parameters for various scenarios.
difsimpars <- tidyr::crossing(
n=seq(5, 100, by = 5),
delta = seq(1,3, by=0.5),
cv_delta = c(0, 0.5),
)And now we run them
if(!file.exists(paste0("../DerivedData/difsims_decomp_",
nsims, ".rds")) || overwrite) {
pb <- progress_bar$new(total = nrow(difsimpars))
difsims <- difsimpars %>%
mutate(sim = 1:nrow(difsimpars)) %>%
group_by(sim) %>%
nest(params = c(n, delta, cv_delta)) %>%
mutate(output = map(params,
~{pb$tick();
bind_rows(purrr::rerun(nsims,
HVPG_dif_sim(.x$n, .x$delta,
.x$cv_delta,
decomp=1)))}))
saveRDS(difsims, paste0("../DerivedData/difsims_decomp_", nsims, ".rds"))
}if(!file.exists(paste0("../DerivedData/difsims_comp_",
nsims, ".rds")) || overwrite) {
pb <- progress_bar$new(total = nrow(difsimpars))
difsims <- difsimpars %>%
mutate(sim = 1:nrow(difsimpars)) %>%
group_by(sim) %>%
nest(params = c(n, delta, cv_delta)) %>%
mutate(output = map(params,
~{pb$tick();
bind_rows(purrr::rerun(nsims,
HVPG_dif_sim(.x$n, .x$delta,
.x$cv_delta,
decomp=2)))}))
saveRDS(difsims, paste0("../DerivedData/difsims_comp_", nsims, ".rds"))
}And extract the results
difsims_decomp <- readRDS(
paste0("../DerivedData/difsims_decomp_", nsims, ".rds"))
difsims_decomp_res <- difsims_decomp %>%
ungroup() %>%
mutate(power = map_dbl(output, ~mean(.x$p.value < 0.05))) %>%
unnest(params) %>%
mutate(delta = as.factor(delta)) %>%
mutate(Effects = ifelse(cv_delta==0, "Homogeneous Effects",
"Heterogeneous Effects")) %>%
mutate(Effects = fct_inorder(Effects)) %>%
mutate(decomp = trt_all$decomp[1])
difsims_comp <- readRDS(
paste0("../DerivedData/difsims_comp_", nsims, ".rds"))
difsims_comp_res <- difsims_comp %>%
ungroup() %>%
mutate(power = map_dbl(output, ~mean(.x$p.value < 0.05))) %>%
unnest(params) %>%
mutate(delta = as.factor(delta)) %>%
mutate(Effects = ifelse(cv_delta==0, "Homogeneous Effects",
"Heterogeneous Effects")) %>%
mutate(Effects = fct_inorder(Effects)) %>%
mutate(decomp = trt_all$decomp[2])
difsims_res <- bind_rows(difsims_comp_res, difsims_decomp_res)Plotting
ggplot(difsims_res, aes(x=n, y=power, colour=delta)) +
geom_point() +
geom_line() +
facet_grid(decomp~Effects) +
coord_cartesian(ylim=c(0.5, 1)) +
scale_color_brewer(type = "qual", palette = 2) +
annotate("rect", ymin = 0.8, ymax = 1, xmin=0,
xmax=100, alpha = .4, fill="grey") +
labs(y="Power", x="Sample Size",
colour="Intervention\nEffect (mmHg)")Required Individuals
And how many people do we need for each scenario?
difsims_80power <- difsims_res %>%
arrange(power) %>%
filter(power > 0.8) %>%
select(decomp, delta, Effects, n) %>%
group_by(delta, Effects, decomp) %>%
slice(1) %>%
arrange(decomp, delta) %>%
rename("Patients" = decomp,
"Difference (mmHg)" = delta,
"80% Power" = n)
difsims_90power <- difsims_res %>%
arrange(power) %>%
filter(power > 0.9) %>%
select(decomp, delta, Effects, n) %>%
group_by(delta, Effects, decomp) %>%
slice(1) %>%
arrange(decomp, delta) %>%
rename("Patients" = decomp,
"Difference (mmHg)" = delta,
"90% Power" = n)
difsims_power <- left_join(difsims_80power, difsims_90power)
decomp_change <- head(
which(
difsims_power$Patients ==
trt_all$decomp[2]), 1)
# kable(difsims_power[,-1]) %>%
# kable_styling("striped", full_width = F) %>%
# pack_rows(trt_all$decomp[1], 1, decomp_change-1) %>%
# pack_rows(trt_all$decomp[2], decomp_change, nrow(difsims_80power))Analytical solution
difsims_ana <- function(Patients, Difference, Effects, Power,
trt_all=trt_all) {
Effects <- as.character(Effects)
Difference <- as.numeric(Difference)
heterogen <- ifelse(Effects=="Homogeneous Effects",
0, 0.5)
decomp = ifelse(Patients=="Includes Decompensated", 1, 2)
trt_all_pat <- trt_all[decomp,]
signvar_sd <- sqrt(
(trt_all_pat$signvar_sd*trt_all_pat$mean)^2 +
(heterogen*Difference)^2)
dz <- Difference/signvar_sd
ceiling(pwr::pwr.t.test(d=dz, sig.level = 0.05, power = Power,
alternative = "greater", type = "paired")$n)
}
difsims_power_ana <- difsims_power %>%
rename(Difference = `Difference (mmHg)`) %>%
mutate(Difference = as.numeric(as.character(Difference)),
Effects= as.character(Effects)) %>%
group_by(Patients, Difference, Effects) %>%
mutate("80% Power"= pmap_dbl(list(Patients, Difference,
Effects), difsims_ana, Power=0.8,
trt_all = trt_all),
"90% Power"= pmap_dbl(list(Patients, Difference,
Effects), difsims_ana, Power=0.9,
trt_all = trt_all))
kable(difsims_power_ana[,-1]) %>%
kable_styling("striped", full_width = F) %>%
pack_rows(trt_all$decomp[1], 1, decomp_change-1) %>%
pack_rows(trt_all$decomp[2], decomp_change, nrow(difsims_power_ana))difpower <- kable(difsims_power_ana[,-1]) %>%
kable_styling("striped", full_width = F) %>%
pack_rows(trt_all$decomp[1], 1, decomp_change-1) %>%
pack_rows(trt_all$decomp[2], decomp_change, nrow(difsims_power_ana))
difpower# save_kable(difpower, "figures/difpower.jpg")Contour Plots
difsims_ana_contour <- function(Patients, Difference, Effects, n,
trt_all=trt_all) {
Effects <- as.character(Effects)
Difference <- as.numeric(Difference)
heterogen <- ifelse(Effects=="Homogeneous Effects",
0, 0.5)
decomp = ifelse(Patients=="Includes Decompensated", 1, 2)
trt_all_pat <- trt_all[decomp,]
signvar_sd <- sqrt(
(trt_all_pat$signvar_sd*trt_all_pat$mean)^2 +
(heterogen*Difference)^2)
dz <- Difference/signvar_sd
pwr::pwr.t.test(d=dz, sig.level = 0.05, n = n,
alternative = "greater", type = "paired")$power
}
contour_dat <- tidyr::crossing(Difference = seq(0.3,3,length.out=2701),
n = 5:80,
Effects = c("Homogeneous Effects",
"Heterogeneous Effects"),
Patients = c("Includes Decompensated",
"Only Compensated"))Run it
contour_power <- contour_dat %>%
mutate(Test = 1:n()) %>%
group_by(Test) %>%
mutate(Power=pmap_dbl(list(Patients, Difference, Effects, n),
difsims_ana_contour, trt_all=trt_all)) %>%
ungroup()
saveRDS(contour_power, "../DerivedData/contour_power.rds")contour_power <- readRDS("../DerivedData/contour_power.rds")
library(viridis)
contour_power <- contour_power %>%
mutate(Power_cut = cut(Power, breaks = seq(0,1, length.out = 11))) %>%
mutate(Power = ifelse(Power == 1, 0.99, Power)) # Note below to explain this
contour_het <- contour_power %>%
filter(Effects!="Homogeneous Effects")
contour_hom <- contour_power %>%
filter(Effects=="Homogeneous Effects")
homplot <- ggplot(contour_hom, aes(x=n, y=Difference, z=Power)) +
geom_contour_filled(alpha=0.8, breaks=seq(0,1, by=0.1)) +
facet_wrap(.~Patients, scales = "free") +
theme_ipsum_rc() +
labs(x = "Sample Size",
y = "Hypothetical True Intervention Effect (mmHg)") +
scale_y_continuous(breaks = seq(0.5, 3, by = 0.5)) +
scale_fill_viridis("Power", discrete = T) +
geom_contour(breaks=0.8, colour="black", linetype="dashed")
hetplot <- ggplot(contour_het, aes(x=n, y=Difference, z=Power)) +
geom_contour_filled(alpha=0.8, breaks=seq(0,1.1, by=0.1)) +
facet_wrap(.~Patients, scales = "free") +
theme_ipsum_rc() +
labs(x = "Sample Size",
y = "Hypothetical True Intervention Effect (mmHg)") +
scale_y_continuous(breaks = seq(0.5, 3, by = 0.5)) +
scale_fill_viridis("Power", discrete = T) +
geom_contour(breaks=0.8, colour="black", linetype="dashed")
homplot
hetplot
ggsave(homplot, height=5, width=10, filename = "figures/Dif_hom_contour.png")
ggsave(hetplot, height=5, width=10, filename = "figures/Dif_het_contour.png")
ggsave(homplot, height=5, width=10, filename = "figures/Dif_hom_contour.jpg",
dpi = 600)
ggsave(hetplot, height=5, width=10, filename = "figures/Dif_het_contour.jpg",
dpi = 600)
# +
# xlab("Minor allele frequency")+
# ylab("Hypothetical effect size")+
# scale_x_log10(expand = c(0, 0), position = "bottom") +
# scale_y_continuous(expand = c(0, 0))+
# geom_line(data = power.80, col = "black")+
# theme_classic(base_size = 12)The strange line of code where I convert those values = 1 to 0.99 is to prevent the graph from showing strangely. I think this has to do with floating point accuracy. Some of the values equal to 1, are rounded in the computer number system to a little bit above 1, and then the plot makes them white. So by setting them to 0.99, they’re still the same colour, but the plot is filled correctly.
Power Analysis for Difference in Differences
Simulation
HVPG_difindif_sim <- function(n, delta1, delta2, cv_delta,
wscv=trt_all$wscv,
mean=trt_all$mean,
cv=trt_all$cv,
decomp ) {
wscv <- wscv[decomp]
mean <- mean[decomp]
cv <- cv[decomp]
var <- (cv*mean)^2
sd_true <- sqrt(var * icc)
pre_true1 <- rnorm(n, mean, sd_true)
pre_true2 <- rnorm(n, mean, sd_true)
pre_meas1 <- pre_true1 + rnorm(n, 0, mean*wscv)
pre_meas2 <- pre_true2 + rnorm(n, 0, mean*wscv)
post_true1 <- pre_true1 - rnorm(n, delta1, cv_delta*delta1)
post_true2 <- pre_true2 - rnorm(n, delta2, cv_delta*delta2)
post_meas1 <- post_true1 + rnorm(n, 0, mean*wscv)
post_meas2 <- post_true2 + rnorm(n, 0, mean*wscv)
measured <- tibble::tibble(
ID = rep(1:n, times=2),
Pre = c(pre_meas1, pre_meas2),
Post = c(post_meas1, post_meas2),
Diff = Post - Pre,
Group = rep(c("A", "B"), each=n)
)
d <- effsize::cohen.d(measured$Diff, measured$Group,
paired=FALSE)$estimate
mod <- lm(Post ~ Pre + Group, data=measured)
testout <- broom::tidy(mod) %>%
filter(term=="GroupB") %>%
select(-term) %>%
mutate(p.value = pt(statistic, mod$df, lower.tail = FALSE))
# Note: using a one-sided p value
out <- mutate(testout, d=d)
return(out)
}Now, we set up the simulation for various scenarios.
difindifsimpars <- tidyr::crossing(
n = c( seq(5, 100, by = 5), seq(110, 200, by=10)),
delta1 = seq(1,3, by = 0.5),
delta2 = seq(0,2, by = 0.5),
cv_delta = c(0, 0.5),
) %>%
mutate(deltadif = delta1 - delta2) %>%
filter(delta1 > delta2)And we run it
# if(!file.exists(paste0("../DerivedData/difindifsims_decomp_",
# nsims, ".rds")) || overwrite) {
#
# pb <- progress_bar$new(total = nrow(difindifsimpars))
#
# difindifsims <- difindifsimpars %>%
# mutate(sim = 1:nrow(difindifsimpars)) %>%
# group_by(sim) %>%
# nest(params = c(n, delta1, delta2, cv_delta)) %>%
# mutate(output = map(params, .progress = TRUE,
# ~{pb$tick();
# bind_rows(purrr::rerun(nsims,
# HVPG_difindif_sim(.x$n, .x$delta1,
# .x$delta2, .x$cv_delta,
# decomp = 1)))}))
#
# saveRDS(difindifsims,
# paste0("../DerivedData/difindifsims_decomp_", nsims, ".rds"))
#
# }# if(!file.exists(paste0("../DerivedData/difindifsims_comp_",
# nsims, ".rds")) || overwrite) {
#
# pb <- progress_bar$new(total = nrow(difindifsimpars))
#
# difindifsims <- difindifsimpars %>%
# mutate(sim = 1:nrow(difindifsimpars)) %>%
# group_by(sim) %>%
# nest(params = c(n, delta1, delta2, cv_delta)) %>%
# mutate(output = map(params,
# ~{pb$tick();
# bind_rows(purrr::rerun(nsims,
# HVPG_difindif_sim(.x$n, .x$delta1,
# .x$delta2, .x$cv_delta,
# decomp = 2)))}))
#
# saveRDS(difindifsims,
# paste0("../DerivedData/difindifsims_comp_", nsims, ".rds"))
#
# }# difindifsims_decomp <- readRDS(paste0("../DerivedData/difindifsims_decomp_", nsims, ".rds"))
#
# difindifsims_decomp_res <- difindifsims_decomp %>%
# ungroup() %>%
# mutate(power = map_dbl(output, ~mean(.x$p.value < 0.05))) %>%
# unnest(params) %>%
# mutate(deltadif = delta1 - delta2,
# delta1 = as.factor(delta1),
# delta2 = as.factor(delta2),
# deltadif = as.factor(deltadif)) %>%
# #filter(deltadif != 0.5) %>%
# mutate(Effects = ifelse(cv_delta==0, "Homogeneous Effects",
# "Heterogeneous Effects")) %>%
# mutate(Effects = fct_inorder(Effects)) %>%
# mutate(decomp = trt_all$decomp[1])
#
#
# difindifsims_comp <- readRDS(paste0("../DerivedData/difindifsims_comp_", nsims, ".rds"))
#
# difindifsims_comp_res <- difindifsims_comp %>%
# ungroup() %>%
# mutate(power = map_dbl(output, ~mean(.x$p.value < 0.05))) %>%
# unnest(params) %>%
# mutate(deltadif = delta1 - delta2,
# delta1 = as.factor(delta1),
# delta2 = as.factor(delta2),
# deltadif = as.factor(deltadif)) %>%
# #filter(deltadif != 0.5) %>%
# mutate(Effects = ifelse(cv_delta==0, "Homogeneous Effects",
# "Heterogeneous Effects")) %>%
# mutate(Effects = fct_inorder(Effects)) %>%
# mutate(decomp = trt_all$decomp[2])
#
#
#
# difindifsims_res <- bind_rows(difindifsims_decomp_res,
# difindifsims_comp_res)Now run in the cluster, and extract the results
difindifsimfiles <- list.files("../Cluster/", pattern = "\\d.rds",
full.names = T)
a <- as.numeric(str_match(difindifsimfiles, pattern = "_comp_(\\d*).rds")[,2])
which(!(1:500 %in% a))
b <- as.numeric(str_match(difindifsimfiles, pattern = "_decomp_(\\d*).rds")[,2])
which(!(1:500 %in% b))
difindifsims <- tibble(file = difindifsimfiles) %>%
mutate(decomp = ifelse(str_detect(file, "_decomp_"),
"Includes Decompensated",
"Only Compensated"),
batch = as.numeric(str_match(file, "(\\d+).rds")[,2]),
sim_add = 50*(batch-1)) %>%
rowwise() %>%
mutate(data = map(file, readRDS))
difindifsims <- difindifsims %>%
ungroup() %>%
unnest(data) %>%
ungroup() %>%
unnest(params) %>%
unnest(output)
difindifsims_res <- difindifsims %>%
group_by(decomp, deltadif, n, delta1, delta2, cv_delta) %>%
summarise(
power = mean(p.value < 0.05),
d = mean(d)
) %>%
ungroup() %>%
mutate(Effects = ifelse(cv_delta==0, "Homogeneous Effects",
"Heterogeneous Effects")) %>%
mutate(delta1 = as.factor(delta1),
delta2 = as.factor(delta2),
deltadif = as.factor(deltadif))
saveRDS(difindifsims_res, "../DerivedData/difindifsims_res.rds")difindifsims_res <- readRDS("../DerivedData/difindifsims_res.rds")
difindifsims_decomp_res <- filter(difindifsims_res,
decomp=="Includes Decompensated")
difindifsims_comp_res <- filter(difindifsims_res,
decomp=="Only Compensated")Plotting
Here we have the size of the effect of the better intervention as the
difindifplot_decomp <-
ggplot(difindifsims_decomp_res, aes(x=n, y=power, colour=delta2)) +
geom_point() +
geom_line() +
facet_grid(delta1~Effects) +
coord_cartesian(ylim=c(0.5, 1)) +
annotate("rect", ymin = 0.8, ymax = 1, xmin=0, xmax=200,
alpha = .4, fill="grey") +
scale_color_brewer(type = "qual", palette = 2) +
labs(y="Power", x="Sample Size",
colour="Reference\nIntervention\nEffect (mmHg)",
title=trt_all$decomp[1]) +
theme(plot.title = element_text(hjust = 0.5))
difindif_legend <- cowplot::get_legend(difindifplot_decomp)
difindifplot_decomp <- difindifplot_decomp +
guides(colour=FALSE)
difindifplot_comp <-
ggplot(difindifsims_comp_res, aes(x=n, y=power, colour=delta2)) +
geom_point() +
geom_line() +
facet_grid(delta1~Effects) +
coord_cartesian(ylim=c(0.5, 1)) +
annotate("rect", ymin = 0.8, ymax = 1, xmin=0, xmax=200,
alpha = .4, fill="grey") +
scale_color_brewer(type = "qual", palette = 2) +
labs(y="Power", x="Sample Size",
colour="Reference\nIntervention\nEffect (mmHg)",
title=trt_all$decomp[2]) +
theme(plot.title = element_text(hjust = 0.5)) +
guides(colour=FALSE)
difindifplot <- cowplot::plot_grid(
difindifplot_decomp, difindifplot_comp, difindif_legend,
nrow = 1, rel_widths = c(3,3,0.5)
)
difindifplot
Required Individuals
And how many people do we need for each scenario?
difindifsims_80power <- difindifsims_res %>%
arrange(power) %>%
filter(power > 0.8) %>%
select(decomp, deltadif, delta1, delta2, Effects, n) %>%
group_by(delta1, deltadif, Effects, decomp) %>%
slice(1) %>%
arrange(decomp, desc(deltadif), desc(delta1), Effects) %>%
rename("Patients" = decomp,
"Intervention 1 Effect (mmHg)" = delta1,
"Intervention 2 Effect (mmHg)" = delta2,
"Difference (mmHg)" = deltadif,
"80% Power" = n)
difindifsims_90power <- difindifsims_res %>%
arrange(power) %>%
filter(power > 0.9) %>%
select(decomp, deltadif, delta1, delta2, Effects, n) %>%
group_by(delta1, deltadif, Effects, decomp) %>%
slice(1) %>%
arrange(decomp, desc(deltadif), desc(delta1), Effects) %>%
rename("Patients" = decomp,
"Intervention 1 Effect (mmHg)" = delta1,
"Intervention 2 Effect (mmHg)" = delta2,
"Difference (mmHg)" = deltadif,
"90% Power" = n)
difindifsims_power <- left_join(difindifsims_80power, difindifsims_90power) %>%
mutate(`90% Power` = as.character(`90% Power`)) %>%
mutate(`90% Power` = ifelse(is.na(`90% Power`),
">200", `90% Power`)) %>%
filter(`Difference (mmHg)` != 0.5)
decomp_change <- head(
which(
difindifsims_power$Patients ==
trt_all$decomp[2]), 1)
kable(difindifsims_power[,-1]) %>%
kable_styling("striped", full_width = F) %>%
pack_rows(trt_all$decomp[1], 1, decomp_change-1) %>%
pack_rows(trt_all$decomp[2], decomp_change, nrow(difindifsims_power))difindiftable_decomp <- difindifsims_power %>%
filter(Patients=="Includes Decompensated") %>%
ungroup() %>%
select(-Patients) %>%
kable() %>%
kable_styling("striped", full_width = F) %>%
pack_rows("Includes Decompensated", 1, decomp_change-1)
difindiftable_comp <- difindifsims_power %>%
filter(Patients=="Only Compensated") %>%
ungroup() %>%
select(-Patients) %>%
kable() %>%
kable_styling("striped", full_width = F) %>%
pack_rows("Only Compensated", 1, decomp_change-1)
difindiftable_decompdifindiftable_comp# save_kable(difindiftable_decomp, "figures/difindifpower_dc.jpg")
# save_kable(difindiftable_comp, "figures/difindifpower_c.jpg")Contour Plot
First let’s look at different deltadif values.
difindifsims_res_hom <- difindifsims_res %>%
filter(cv_delta==0) %>%
mutate(delta1 = as.numeric(as.character(delta1)),
delta2 = as.numeric(as.character(delta2)),
deltadif = as.numeric(as.character(deltadif))) %>%
mutate(power = ifelse(power == 1, 0.99, power))
difindifsims_res_het <- difindifsims_res %>%
filter(cv_delta!=0) %>%
mutate(delta1 = as.numeric(as.character(delta1)),
delta2 = as.numeric(as.character(delta2)),
deltadif = as.numeric(as.character(deltadif))) %>%
mutate(power = ifelse(power == 1, 0.99, power))
difindif_cont1_hom <- difindifsims_res_hom %>%
filter(deltadif!=3) %>%
ggplot(aes(x=n, y=delta1, z=power)) +
geom_contour_filled(alpha=0.8, breaks=seq(0,1.1, by=0.1)) +
facet_grid(deltadif~decomp, scales = "free") +
theme_ipsum_rc() +
labs(x = "Sample Size",
y = "Hypothetical Intervention Effect of Main Treatment (mmHg)",
subtitle = "Comparison of Differences of Effects between Interventions") +
scale_y_continuous(breaks = seq(0.5, 5, by = 0.5)) +
scale_fill_viridis("Power", discrete = T) +
geom_contour(breaks=0.8, colour="black", linetype="dashed")
difindif_cont1_hom
difindif_cont1_het <- difindifsims_res_het %>%
filter(deltadif!=3) %>%
ggplot(aes(x=n, y=delta1, z=power)) +
geom_contour_filled(alpha=0.8, breaks=seq(0,1.1, by=0.1)) +
facet_grid(deltadif~decomp, scales = "free") +
theme_ipsum_rc() +
labs(x = "Sample Size",
y = "Hypothetical Intervention Effect of Main Treatment (mmHg)",
subtitle = "Comparison of Differences of Effects between Interventions") +
scale_y_continuous(breaks = seq(0.5, 5, by = 0.5)) +
scale_fill_viridis("Power", discrete = T) +
geom_contour(breaks=0.8, colour="black", linetype="dashed")
difindif_cont1_het
This is helpful to visualise, though probably not for the paper. With homogeneous effects, the determinant of the power is the difference in intervention effects; it’s a straight line. With heterogeneous effects, the line is not straight
difindif_cont2_hom <- ggplot(difindifsims_res_hom, aes(x=n, y=delta1, z=power)) +
geom_contour_filled(alpha=0.8, breaks=seq(0,1.1, by=0.1)) +
facet_grid(delta2~decomp, scales = "free") +
theme_ipsum_rc() +
labs(x = "Sample Size",
y = "Hypothetical Intervention Effect of Main Treatment (mmHg)",
subtitle = "Comparisons Grouped by Intervention Effects of the Reference Treatment (mmHg)") +
scale_y_continuous(breaks = seq(0.5, 5, by = 0.5)) +
scale_fill_viridis("Power", discrete = T) +
geom_contour(breaks=0.8, colour="black", linetype="dashed")
difindif_cont2_hom
difindif_cont2_het <- ggplot(difindifsims_res_het, aes(x=n, y=delta1, z=power)) +
geom_contour_filled(alpha=0.8, breaks=seq(0,1.1, by=0.1)) +
facet_grid(delta2~decomp, scales = "free") +
theme_ipsum_rc() +
labs(x = "Sample Size",
y = "Hypothetical Intervention Effect of Main Treatment (mmHg)",
subtitle = "Comparisons Grouped by Intervention Effects of the Reference Treatment (mmHg)") +
scale_y_continuous(breaks = seq(0.5, 5, by = 0.5)) +
scale_fill_viridis("Power", discrete = T) +
geom_contour(breaks=0.8, colour="black", linetype="dashed")
difindif_cont2_het
And just looking against placebo (i.e. delta2=0)
difindif_cont3_hom <- difindifsims_res_hom %>%
filter(deltadif!=3) %>%
filter(delta2==0) %>%
ggplot(aes(x=n, y=delta1, z=power)) +
geom_contour_filled(alpha=0.8, breaks=seq(0,1.1, by=0.1)) +
facet_wrap(.~decomp, scales = "free") +
theme_ipsum_rc() +
labs(x = "Sample Size",
y = "Hypothetical Intervention Effect of Main Treatment (mmHg)") +
scale_y_continuous(breaks = seq(0.5, 5, by = 0.5)) +
scale_fill_viridis("Power", discrete = T) +
geom_contour(breaks=0.8, colour="black", linetype="dashed") +
xlim(c(5,120))
difindif_cont3_hom
difindif_cont3_het <- difindifsims_res_het %>%
filter(deltadif!=3) %>%
filter(delta2==0) %>%
ggplot(aes(x=n, y=delta1, z=power)) +
geom_contour_filled(alpha=0.8, breaks=seq(0,1.1, by=0.1)) +
facet_wrap(.~decomp, scales = "free") +
theme_ipsum_rc() +
labs(x = "Sample Size",
y = "Hypothetical Intervention Effect of Main Treatment (mmHg)") +
scale_y_continuous(breaks = seq(0.5, 5, by = 0.5)) +
scale_fill_viridis("Power", discrete = T) +
geom_contour(breaks=0.8, colour="black", linetype="dashed") +
xlim(c(5,120))
difindif_cont3_het
ggsave(difindif_cont3_hom, height=5, width=10, filename = "figures/Difindif_hom_contour.png")
ggsave(difindif_cont3_het, height=5, width=10, filename = "figures/Difindif_het_contour.png")
ggsave(difindif_cont3_hom, height=5, width=10, filename = "figures/Difindif_hom_contour.jpg",
dpi = 600)
ggsave(difindif_cont3_het, height=5, width=10, filename = "figures/Difindif_het_contour.jpg",
dpi = 600)ICC Figures
colours <- c("#61b096", "#bd7969")
make_distributions <- function(icc) {
sd_true <- 1
var_true <- sd_true^2
var_tot <- var_true / icc
sd_tot <- sqrt(var_tot)
sd_error <- sqrt(var_tot - var_true)
distrib <- ggplot(data.frame(x=c(-5,5)), aes(x=x)) +
stat_function(fun = dnorm,
colour = "black", size = 1.5, args = list(mean = 0, sd=sd_tot),
geom = "line") +
stat_function(fun = dnorm,
colour = colours[1], size = 1, args = list(mean = 0, sd=sd_true),
geom = "line") +
stat_function(fun = dnorm,
colour = colours[2], size = 1, args = list(mean = 0, sd=sd_error),
geom = "line") +
geom_vline(xintercept = 0, linetype="dashed") +
theme(axis.title.x = element_blank(),
axis.title.y = element_blank(),
axis.text.y=element_blank(),
axis.ticks.y=element_blank(),
axis.text.x=element_blank(),
panel.grid.major = element_blank(),
panel.grid.minor = element_blank()) +
annotate("text", x=2.5, y=0.5,
label="Error\nVariance",
colour = colours[2], hjust=0.5) +
annotate("text", x=-2.5, y=0.5,
label="True\nVariance",
colour = colours[1], hjust=0.5) +
coord_cartesian(ylim=c(0,0.7))
return(distrib)
}
make_piecharts <- function(icc) {
sd_true <- 1
var_true <- sd_true^2
var_tot <- var_true / icc
sd_tot <- sqrt(var_tot)
var_error <- var_tot - var_true
var_pie <- data.frame(Variance = c("True", "Error"),
Values = c(var_true, var_error))
var_pie$Variance <- forcats::fct_inorder(var_pie$Variance)
pie <- ggplot(var_pie, aes(x="", y=Values, fill=Variance))+
geom_bar(width = 1, stat = "identity") +
theme(axis.text.y=element_blank(),
axis.ticks.y=element_blank(),
axis.text.x=element_blank(),
axis.ticks.x=element_blank(),
panel.grid.major = element_blank(),
panel.grid.minor = element_blank()) +
coord_polar("y", start=0) +
scale_fill_manual(values = colours) +
labs(x="", y="") +
guides(fill=FALSE) +
#labs(title=paste0("ICC=", icc)) +
NULL
return(pie)
}
make_distrib_and_pie <- function(icc) {
dist <- make_distributions(icc)
pie <- make_piecharts(icc)
outplot <- cowplot::plot_grid(pie, dist, rel_widths = c(1,2)) +
draw_figure_label(paste0("ICC=", icc))
return(outplot)
}
comparison_charts <- tibble(
icc = c(0.1, 0.3, 0.7, 0.9)
) %>%
mutate(chart = purrr::map(icc, make_distrib_and_pie))
plot_grid(plotlist = comparison_charts$chart, ncol=1)